The group has faced criticism for political statements seeming to glorify militant groups such as Hamas and Hezbollah.
Hungary previously banned the group.
Liberal MP Vince Gasparro, parliamentary secretary for combating crime, said Kneecap has "publicly displayed support for terrorist organisations such as Hezbollah and Hamas" that goes beyond artistic expression.
"Canada stands firmly against hate speech, incitement to violence and the glorification of terrorism," Gasparro said in a video on social media.
"Political debate and free speech are vital to our democracy, but open endorsements of terrorist groups are not free speech."
Kneecap has accused critics of trying to silence the band because of its support for the Palestinian cause throughout Israel's war in Gaza.
They say they do not support Hezbollah and Hamas nor condone violence.
Kneecap responded in an Instagram post, saying that Gasparro's comments are "wholly untrue and deeply malicious".
"We have today instructed our lawyers to initiate legal action against you," the band's statement said.
"We will be relentless in defending ourselves against baseless accusation to silence our opposition to a genocide being committed by Israel."
Kneecap was scheduled to perform in October in Toronto and Vancouver.
The Canada-based advocacy organization Centre for Israel and Jewish Affairs says the decision is a stand against "incitement, hate and radicalization," while Jewish organisation B'nai Brith is declaring "victory".
Kneecap performed in April at the Coachella Valley Music and Arts Festival in California, where they accused Israel - enabled by the US government - of committing genocide against the Palestinians.
That sparked calls for the rappers' US visas to be revoked and several Kneecap gigs have since been cancelled as a result.
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